I was once again distracted by something ridiculous in the HNQ sidebar: [Scientific applications of the tikzducks][1]

One answer states that It is possible to form a grammatical English sentence of length n, using only the words "duck" and "ducks", for all values of n.

I'm having a hard time understanding the sentences of length 4 and above. What exactly do they mean and why are they grammatically correct? I tried replacing part of the sentence tree with something else, such as "cows moo", but the resulting sentence "Ducks cows moo duck" does not seem to have any meaning. [1]: https://tex.stackexchange.com/a/423089